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Rationalize the denominator of √3+√2\ 5+√2 ​
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21 votes
Rationalize the denominator of √3+√2\ 5+√2 ​

User Jazmit
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1 Answer

13 votes
13 votes

Answer:


( 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2)/(23)

Explanation:


(\sqrt3 \ + \ \sqrt2 )/(5 \ + \ \sqrt2 ) \\\\=(\sqrt3 \ + \ \sqrt2 )/(5 \ + \ \sqrt2 ) * (5 \ - \ \sqrt2 )/(5 \ - \ \sqrt2 ) \\\\=(( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2))/((5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 ))\\\\=(( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2))/((5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 ))\\\\=(5 \sqrt3 \ + \ 5\sqrt 2 \ - \ √( 3* 2 ) \ - \ √(2 * 2))/((5)^2 \ - \ (\sqrt2)^2)\\\\= ( 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2)/(25 - 2)\\\\


= ( 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2)/(23)

User Pitosalas
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